March 11, 2011

Today’s problem appears with some regularity at places like Proggit and Stack Overflow and in lists of programming interview questions:

Given a binary tree t and two elements of the tree, m and n, with m<n, find the lowest element of the tree (farthest from the root) that is an ancestor of both m and n.

For example, in the tree shown at right, the lowest common ancestor of 4 and 7 is 6, the lowest common ancestor of 4 and 10 is 8, and the lowest common ancestor of 1 and 4 is 3. It is possible for an element of the tree to be its own ancestor, so the lowest common ancestor of 1 and 3 is 3, and the lowest common ancestor of 3 and 6 is 3.

Your task is to write a function that finds the lowest common ancestor of two elements of a binary tree. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.